SwissTournament/accelerated pairings

Accelerated Pairings can be used in Swiss tournaments if the strength of the top players is much higher than the rest of the field.

It is helpful to prevent the top players from not playing each other, something that in general is a bad thing.

The underlying idea is that:

- in round 1 games are between players allocated in rank bands

- in round 2 the losers of the games between higher ranked players will play games against the winners of the games between lower ranked players, and are expected to win, so that after round 2 fewer players will have an score of 2 wins.

McMahon pairing can be seen as an extreme case of this: the players won't even play each other as it is assumed that the weaker player will lose. (The difference in McMahon score is the number of games the weaker player is supposed to have lost against the higher ranked player.)

Examples of a 24 player tournament

There are 2 main ways to do accelerated pairings: in four groups and in 6 groups.

In principle it can be done with any number of 2n groups but accelerated pairing can lead to more players with 2 wins. (See the overview at the end)

Setup with 4 groups

Group A the highest ranked 6 players (P1 - P6)
Group B the next highest ranked 6 players (P7 - P12)
Group C the next highest ranked 6 players (P13 - P18)
Group D the next highest ranked 6 players (P19 - P24)

Round 1:

Group A vs B

Board 1 P1  - P7    :W1 = winner L1 = loser
Board 2 P2  - P8    :W2 = winner L2 = loser
Board 3 P3  - P9    :W3 = winner L3 = loser
Board 4 P4  - P10   :W4 = winner L4 = loser
Board 5 P5  - P11   :W5 = winner L5 = loser
Board 6 P6  - P12   :W6 = winner L6 = loser

Group C vs D

Board 7 P13 - P19  :W7  = winner L7 = loser
Board 8 P14 - P20  :W8  = winner L8 = loser
Board 9 P15 - P21  :W9  = winner L9 = loser
Board10 P16 - P22  :W10 = winner L10 = loser
Board11 P17 - P23  :W11 = winner L11 = loser
Board12 P18 - P24  :W12 = winner L12 = loser

Round 2:

winners from A vs B

Board 1 W1 - W4
Board 2 W2 - W5
Board 3 W3 - W6

Losers from A vs B are paired against winners C vs D

Board 4 L1 - W7
Board 5 L2 - W8
Board 6 L3 - W9
Board 7 L4 - W10
Board 8 L5 - W11
Board 9 L6 - W12

losers C vs D play each other

Board 10 L7 - L10
Board 11 L8 - L11
Board 12 L9 - L12

Setup with 6 groups

Group A the highest ranked 4 players (P1 - P4)
Group B the next highest ranked 4 players (P5 - P8)
Group C the next highest ranked 5 players (P9 - P12)
Group D the next highest ranked 5 players (P13 - P16)
Group E the next highest ranked 5 players (P17 - P20)
Group F the next highest ranked 5 players (P21 - P24)

Round 1:

Group A vs B

Board 1 P1  - P5    :W1 = winner L1 = loser
Board 2 P2  - P6    :W2 = winner L2 = loser
Board 3 P3  - P7    :W3 = winner L3 = loser
Board 4 P4  - P8    :W4 = winner L4 = loser

Group C vs D

Board 5 P9  - P13   :W5 = winner L5 = loser
Board 6 P10 - P14   :W6 = winner L6 = loser
Board 7 P11 - P15   :W7 = winner L7 = loser
Board 8 P12 - P16   :W8 = winner L8 = loser

Group E vs F

Board 9 P17 - P21   :W9  = winner L9 = loser
Board10 P18 - P22   :W10 = winner L10 = loser
Board11 P19 - P23   :W11 = winner L11 = loser
Board12 P20 - P24   :W12 = winner L12 = loser

Round 2:

winners from A vs B

Board 1 W1 - W3
Board 2 W2 - W4

Losers from A vs B are paired against winners C vs D

Board 3 l1 - W5
Board 4 L2 - W6
Board 4 L3 - W7
Board 5 L4 - W8

Losers from C vs D are paired against winners E vs F

Board 6 L5 - W9
Board 7 L6 - W10
Board 8 L7 - W11
Board 9 L8 - W12

losers E vs F play each other

Board 10 L9  - L11
Board 11 L10 - L12

From round 3 onwards the normal pairings can be used (and if everything goes according to plan after round 5 the winner can be announced.)

Overview

If the ranking was right to start with after 2 rounds we would have fewer players with 2 wins. If the start rating was mistaken then accelerated pairing can lead to more players with 2 wins than normal Swiss pairing. Below is an overview.

                               Normal             Accelerated
                               Swiss        4 groups      6 groups
Players with 2 wins              6              3             2
Expected players with  1 Win    12             18            20
Expected players with no Win     6              3             2

Maximum  players with  2 Win     6              9            10
Maximum  players with  1 Win    12             18            20
Maximum  players with no Win     6              9            10

Minimum  players with  2 Win     6              3             2
Minimum  players with  1 Win    12              6             4
Minimum  players with no Win     6              3             2